For a positive integer $N$, let $X_0^*(N)$ denote the quotient curve of $X_0(N)$ by the Atkin-Lehmer involutions. In this paper, we determine the trigonality of $X_0^*(N)$ for all $N$. It turns out that there are seven values of $N$ for which $X_0^*(N)$ is a non-trivial trigonal curve.
"Trigonal modular curves $X_0^*(N)$." Proc. Japan Acad. Ser. A Math. Sci. 76 (6) 83 - 86, June 2000. https://doi.org/10.3792/pjaa.76.83